Consider a large disk of radius $$R$$ and two smaller disks, each of radius $$r=R/50$$, lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular separation $$\Delta\theta$$ between their centers. They are made to roll without slipping in opposite directions, with constant angular velocities $$\omega$$ and $$2\omega$$ while the large disk is held stationary. The time $$\tau$$ at which the smaller disks are again in contact is:

[Use $$\sin(\Delta\theta)=\Delta\theta$$ and ignore gravity.]